Nonlinear Elasticity
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Nonlinear Problems of Elasticity
Author: Stuart Antman
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-14
The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.
Nonlinear Elasticity
Author: Y. B. Fu
language: en
Publisher: Cambridge University Press
Release Date: 2001-05-07
Nonlinear elasticity is concerned with nonlinear effects associated with deformations of elastic bodies subjected to external forces or temperature variations. It has important applications in many areas, including the aerospace and rubber industries, and biomechanics. This book, written by a group of leading researchers invited especially for the purpose, provides an up-to-date and concise account of the fundamentals of the theory of nonlinear elasticity and a comprehensive review of several major current research directions in this important field. It combines the characteristics of coherence and detail found in standard treatises with the strength and freshness of research articles. The emphasis is placed firmly on coverage of modern topics and recent developments rather than on the very theoretical approach often found. The book will be an excellent reference source for both beginners and specialists in engineering, applied mathematics and physics. It is also ideally suited for graduate courses.
Nonlinear Elasticity
This textbook provides a rigorous yet accessible introduction to Nonlinear Elasticity aimed at undergraduate students in a compact text. Rooted in concepts from first- and second-year undergraduate Linear Algebra and Calculus (and very little Tensor Algebra), the book touches upon all the fundamental aspects of nonlinear elasticity, from the analysis of deformation and stress, to the constitutive response and modelling of soft solids, to the lab experiments required to obtain their material properties, and to the concepts of equilibrium and energy minimization. Nonlinear Elasticity is an elegant, physics-based, mathematical theory, one usually only available at graduate level to students in advanced studies of engineering, applied mathematics, and theoretical physics. Over the past ten years, the authors developed a classroom-tested pedagogy aimed at narrowing the range of the skills required to approach Nonlinear Elasticity from the perspective of an undergraduate student pursuing a Bachelor of Science or Engineering, as displayed in this book. It concludes with an analysis of several worked examples, spanning a variety of problems of high technical importance and relevance. The book is organized for use as a core text in the classroom or as a self-contained guide of (24 lectures) for independent learning.